scholarly journals Integrated random processes exhibiting long tails, finite moments, and power-law spectra

2001 ◽  
Vol 64 (1) ◽  
Author(s):  
Jaume Masoliver ◽  
Miquel Montero ◽  
Alan McKane
Keyword(s):  
Power Law ◽  
Random Processes ◽  
Long Tails ◽  
Finite Moments

ON THE UBIQUITY OF 1/f NOISE

1989 ◽  
Vol 03 (06) ◽  
pp. 795-819 ◽  
Author(s):  
BRUCE J. WEST ◽  
MICHAEL F. SHLESINGER
Keyword(s):  
Power Law ◽  
Limit Distribution ◽  
Cardiac Activity ◽  
Scientific Productivity ◽  
Random Processes ◽  
Probability Limit ◽  
Mild Conditions ◽  
Inverse Power Law ◽  
Log Normal ◽  
Log Normal Distribution

A generic mechanism for the ubiquitous phenomenon of 1/f noise is reviewed. This mechanism arises in random processes expressible as a product of several random variables. Under mild conditions this product form leads to the log-normal distribution which we show straightforwardly generates 1/f noise. Thus, 1/f noise is tied directly to a probability limit distribution. A second mechanism involving scaling is introduced to provide a natural crossover from log-normal to inverse power-law behavior and generates 1/fα noise instead of pure 1/f noise. Examples of these distributions and the transitions between them are drawn from such diverse areas as economics, scientific productivity, bronchial structure and cardiac activity.

Analysis of power law assumptions for short-period comets and Kuiper bodies

1999 ◽  
Vol 173 ◽  
pp. 289-293 ◽  
Author(s):  
J.R. Donnison ◽  
L.I. Pettit
Keyword(s):  
Power Law ◽  
Pareto Distribution ◽  
Limited Data ◽  
Short Period ◽  
Probability Plots ◽  
Exponential Probability

AbstractA Pareto distribution was used to model the magnitude data for short-period comets up to 1988. It was found using exponential probability plots that the brightness did not vary with period and that the cut-off point previously adopted can be supported statistically. Examination of the diameters of Trans-Neptunian bodies showed that a power law does not adequately fit the limited data available.

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